Problem 3.3, Exploring Patterns. Unit: Accentuate the negative. Big Idea Negative numbers help us to model many real world situations. Essential Question #3: How do I find the difference between integers?
a. Describe any patterns you observe in the way the differences change as the integers subtracted from -10 get smaller.
The results get smaller by one every time the subtracted integer gets smaller by one.
b. Use the patterns you observed to predict the answer to -10 - -1. Check your answer by using a chip board or a number line.
-10 - -1 = -9
c. Predict the answer to -10 - -6. Explain your reasoning.
-10 - -6 = -4
I predicted this answer because the subtracted number is -6 so the answer had to be -4 according to the pattern shown above.
2. When you add two negative integers, you get a negative sum. When you subtract two negative integers. do you always get a negative
difference? Explain.
If the subtracted integer is smaller than the first integer, it will be positive, if not, it will be negative.
Big Idea
Negative numbers help us to model many real world situations.
Essential Question #3: How do I find the difference between integers?
15 - 5 = 10
15 - 4 = 11
15 - 3 = 12
15 - 2 = 13
15 - 1 = 14
15 - 0 = 15
A. Describe any patterns you observe in the way the differences change as the integers subtracted from 15 get smaller.
The results get bigger by one every time the subtracted integer gets smaller by one.
B. Use the patterns you observed to predict the answer to 15 - -1. Check you work using a number line or chip board.
15 - -1 = +16
C. Predict the answer to 15 - -4. Explain your reasoning.
15- -4 = +19
I predicted that answer because a double negative is a positive so 15 - -4 is like 15 + 4 as well and 15 + 4 is 19.
Follow Up:
1.
-10 - 5 = -15
-10 - 4 = -14
-10 - 3 = -13
-10 - 2 = -12
-10 - 1 = -11
-10 - 0 = -10
a. Describe any patterns you observe in the way the differences change as the integers subtracted from -10 get smaller.
The results get smaller by one every time the subtracted integer gets smaller by one.
b. Use the patterns you observed to predict the answer to -10 - -1. Check your answer by using a chip board or a number line.
-10 - -1 = -9
c. Predict the answer to -10 - -6. Explain your reasoning.
-10 - -6 = -4
I predicted this answer because the subtracted number is -6 so the answer had to be -4 according to the pattern shown above.
2. When you add two negative integers, you get a negative sum. When you subtract two negative integers. do you always get a negative
difference? Explain.
If the subtracted integer is smaller than the first integer, it will be positive, if not, it will be negative.
Ex: -9 - -5 = -4
-8 - -10 = +2